Question

In this week's experiment, you send an unpolarized light beam through two polarizers in series. You orient the first polarizer so that its marks indicating its polarization axis are vertical. You then rotate the second polarizer until the intensity of light transmitted through the second polarizer is zero. In this condition, the second polarizer angular scale reads 104.3 degrees and the marks on the second polarizer lie along a line with a 2 degree angle to the horizontal. (a) What is the angle between the two polarizer polarization axes in this condition? (b) If you want to set the angle between the two polarization axes to 20 degrees, you should (i) set the second polarizer so that its marks point in a direction 20 degrees away from the vertical direction. _ (ii) set the second polarizer so that its marks point in a direction 20 degrees away from the horizontal direction. (iii) set the second polarizer so that its angular scale reads 20.0 degrees. (iv) set the second polarizer so that its angular scale reads 70.0 degrees. (v) set the second polarizer so that its angular scale reads 84.3 degrees. (vi) set the second polarizer so that its angular scale reads 34.3 degrees.

Answer 1

Answer:

Part a)

$\theta = 90 degree$

so the polarization axis of two polarizers must be at 90 degree

Part b)

$\theta = 20 + 14.3 = 34.3 degree$

(vi) set the second polarizer so that its angular scale reads 34.3 degrees.

Explanation:

Part 1)

As per law of Malus we know that the intensity of light coming from the second polarizer and the intensity of the light from first polarizer is related as

$I = I_o cos^2\theta$

now we know that we rotate the second polarizer till the intensity of the light becomes zero

so we will have

$I = 0$

so we will have

$\theta = 90 degree$

so the polarization axis of two polarizers must be at 90 degree

Part b)

when two axis are inclined at 90 degree then scale reads 104.3 degree

so here the scale exceeds the reading by

$\Delta \theta = 104.3 - 90 = 14.3$

so in order to make them inclined at 20 degree we will have

$\theta = 20 + 14.3 = 34.3 degree$

(vi) set the second polarizer so that its angular scale reads 34.3 degrees.